Finite Group Databasebeta

← #21458503

Subgroups — #21458503

Order 7808.

336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840487C211yesmaximal, characteristic, complemented
2#16840482C211yesmaximal, characteristic
3#16840115C212yesmaximal
4#16840114C211yesmaximal, characteristic, complemented
5#16840068C212yesmaximal, complemented
6#16839983C212yesmaximal
7#16839973C211yesmaximal, characteristic, complemented
8#16839886C211yesmaximal, characteristic, complemented
9#16839856C212yesmaximal, complemented
10C4×#11758200C211yesmaximal, characteristic
11C61×#474C211yesmaximal, characteristic
12C2×Dic244C2212yes—
13C2×#11758200C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519775—21no—
16#14519770—22no—
17#14519768C2212yes—
18#14519767—22no—
19#14519764C2212yes—
20#14519756—21no—
21Q8×Dic61—21no—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24#14519742C2212yes—
25#14519742C2212yes—
26#14519736—21no—
27#14519708C2211yescharacteristic
28#14519706C2212yes—
29#14519702C2212yes—
30#14519700C2212yes—
31#14519700C2211yescharacteristic
32#14519700C2212yes—
33#14519698C2211yescharacteristic
34C4×#92418C2211yescharacteristic
35C8×Dic61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4×D4×C61C2211yescharacteristic
38#107×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#102×C61C2212yes—
41C2×Q8×C61—21no—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C2×Dic122D411yescharacteristic
45C2×Dic122C2312yes—
46C2×Dic122C2311yescharacteristic
47C2×C8×C61C2312yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61C2312yes—
50C4⋊C4×C61C2311yescharacteristic
51C22⋊C4×C61—21no—
52C42×C61C2311yescharacteristic
53C22⋊Dic61—22no—
54C22⋊Dic61—22no—
55#11758200—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—22no—
59C4⋊Dic61D411yescharacteristic
60C4⋊Dic61C2311yescharacteristic
61#11758196—21no—
62#11758196—22no—
63#11758196—22no—
64#11758196—22no—
65#11758196D412yes—
66C4×Dic61—21no—
67C4×Dic61—22no—
68C4×Dic61—22no—
69C4×Dic61C2312yes—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72Dic244—24no—
73C23×C61—21no—
74Q8×C61—42no—
75D4×C61—21no—
76D4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—42no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D412yes—
88Dic122—22no—
89Dic122—21no—
90Dic122—22no—
91Dic122—22no—
92Dic122#4112yes—
93C8×C61—22no—
94#92418—21no—
95#92418—21no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61C22×D411yescharacteristic
100C4×C61—21no—
101C4×C61—41no—
102C4×C61—42no—
103C4×C61#13512yes—
104C4×C61C2×#4111yescharacteristic
105C4×C612−1+411yescharacteristic
106Dic61—22no—
107Dic61—22no—
108Dic61—22no—
109Dic61—42no—
110Dic61—41no—
111#3364—611nomaximal, Sylow
112C2×C61—81no—
113C2×C61#54811yescharacteristic
114C2×C61C2×#13511yescharacteristic
115C2×C61#57811yescharacteristic
116#557—611no—
117#556—611no—
118#488—612no—
119#487—611no—
120#479—612no—
121#474D6111yescharacteristic
122#464—612no—
123#462—611no—
124C8×Q8—611no—
125C4×Q16—612no—
126C4×SD16—611no—
127C61#336411yescharacteristic, complemented, Sylow
128C2×Q16—612no—
129C2×SD16—611no—
130C4⋊Q8—611no—
131C4⋊Q8—1221no—
132C4⋊Q8C2×D6111yescharacteristic
133#126—1222no—
134#125—612no—
135#125—1222no—
136#124—612no—
137C22⋊Q8—1221no—
138C4×Q8—611no—
139C4×Q8—612no—
140C4×Q8—612no—
141C4×Q8—611no—
142C4×Q8—1221no—
143C4×D4C2×D6111yescharacteristic
144#117—1221no—
145#107C2×D6112yes—
146#106—611no—
147C4⋊C8—612no—
148C4⋊C8C2×D6111yescharacteristic
149#103—612no—
150#103—611no—
151#103—612no—
152#103—612no—
153#102—611no—
154#102C2×D6112yes—
155C4×C8—612no—
156C4×C8—611no—
157C2×Q8—21no—
158C2×Q8—611no—
159C2×Q8—611no—
160C2×Q8—612no—
161C2×D4C22×D6111yescharacteristic
162C22×C4—21no—
163Q16—1224no—
164SD16—1222no—
165C2×C8—611no—
166C2×C8—611no—
167C2×C8C22×D6112yes—
168C4⋊C4—21no—
169C4⋊C4—612no—
170C4⋊C4—611no—
171C4⋊C4—611no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C4⋊C4—1221no—
179C4⋊C4C22×D6112yes—
180C4⋊C4C22×D6111yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C42—612no—
185C42—1222no—
186C42—1222no—
187C42—1221no—
188C42C22×D6111yescharacteristic
189C23—21no—
190Q8—42no—
191Q8—612no—
192Q8—1221no—
193Q8—1222no—
194Q8—1222no—
195Q8—1222no—
196D4—21no—
197D4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—612no—
202C2×C4—612no—
203C2×C4—1221no—
204C2×C4—1222no—
205C2×C4—1221no—
206C2×C4D4×D6111yescharacteristic
207C2×C4D4×D6111yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—22no—
210C8—1221no—
211C8—1221no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22C2×D4×D6111yescharacteristic
216C4—21no—
217C4—41no—
218C4—42no—
219C4—1222no—
220C4—1222no—
221C4—1222no—
222C4—2441no—
223C4—2442no—
224C4#1451979612yes—
225C4#41×D6111yescharacteristic
226C4#1451982511yescharacteristic
227C2—81no—
228C2#1684042211yescharacteristic
229C2C2×#1451979611yescharacteristic
230C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3364
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16840487C2semidirect
4. #16840114C2semidirect
5. #16840068C2semidirect
7. #16839973C2semidirect
8. #16839886C2semidirect
9. #16839856C2semidirect
127. C61#3364semidirect